Assuming this individual doesn't require basic needs (eating, drinking, etc...), and he can't feel any other needs like, the need for love, the need to be alone for a moment, the need to seek accomplishment, fame, money, etc... He doesn't require any needs whatsoever.
Are there any reasons for this individual to stay alive?
See also: What is the motivation of all individuals to stay alive?
No, this individual is way beyond its expiration date and can expire, already has. Seems a pretty straightforward deduction. If this maximally ascetic being has no needs, it has no need to stay alive, which requires needful motivation.
The question, then, is whether a "reason" can exist without a "need." I would say the two can't be clearly distinguished, even in AI. You might say a machine can perform reasoning without needs, but machines clearly have operational "needs," even apart from programmed values, whether or not they recognize it.
What you may really be asking is whether life is meaningful without desires or recognized needs or, in philosophical terms, a teleology, though these are not exactly the same. Most people today have abandoned an Aristotelean teleology in which even rocks may have "needs" or preferred states.
I would be hard pressed to find any satisfactory definition of "life" that does not include "needs," whether recognized or not. However, there can perhaps be needs without reasons, since reasoning is a need at a higher, symbolic level of recursion.
As to Conifold's suggestion, this dispassion would certainly not apply to most Gods, especially the Abrahamic Gods, who seem to need utterly unreasonable things all the time! It does apply to the Aristotelean deity, which is more like an equilibrium or symmetry of motion.
The problem lies in finding a restrictive definition of the term "need." In any case, I'd say your guy can kick the bucket without having to explain anything.
Yes, to be sure he actually doesn't require any needs.
For instance he is assuming that he doesn't need love on the basis of the limited experience accumulated in his lifetime. As a rational being, until he experience all possible love situations he should always assign a non zero probability to "I do need love". He should try to experience all possible situations and updates his beliefs accordingly. Given the long list of possible needs and the possible situations for every needs, he has plenty of work to do!
Let me also add another way to answer this. Are there any reasons for this individual to die? I would argue that everything else being indifferent, living is superior to dying (assuming that dying implies stopping any activity), as you can always later choose to die, but not viceversa.
